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This paper develops a mathematical model to investigate the Human Immunodeficiency Virus (HIV) infection dynamics. The model includes two transmission modes (cell-to-cell and cell-free), two adaptive immune responses (cytotoxic T-lymphocyte (CTL) and antibody), a saturated CTL immune response, and latent HIV infection. The existence and local stability of equilibria are fully characterized by four reproduction numbers. Through sensitivity analyses, we assess the partial rank correlation coefficients of these reproduction numbers and identify that the infection rate via cell-to-cell transmission, the number of new viruses produced by each infected cell during its life cycle, the clearance rate of free virions, and immune parameters have the greatest impact on the reproduction numbers. Additionally, we compare the effects of immune stimulation and cell-to-cell spread on the model's dynamics. The findings highlight the significance of adaptive immune responses in increasing the population of uninfected cells and reducing the numbers of latent cells, infected cells, and viruses. Furthermore, cell-to-cell transmission is identified as a facilitator of HIV transmission. The analytical and numerical results presented in this study contribute to a better understanding of HIV dynamics and can potentially aid in improving HIV management strategies. [ABSTRACT FROM AUTHOR]

In this paper, we study a mathematical model of Hepatitis C Virus (HCV) infection. We present a compartmental mathematical model involving healthy hepatocytes, infected hepatocytes, non-activated dendritic cells, activated dendritic cells and cytotoxic T lymphocytes. The derivative used is of non-local fractional order and with non-singular kernel. The existence and uniqueness of the system is proven and its stability is analyzed. Then, by applying the Laplace Adomian decomposition method for the fractional derivative, we present the semi-analytical solution of the model. Finally, some numerical simulations are performed for concrete values of the parameters and several graphs are plotted to reveal the qualitative properties of the solutions. [ABSTRACT FROM AUTHOR]

Human immunodeficiency virus (HIV) and human T-lymphotropic virus type I (HTLV-I) are two retroviruses that infect the susceptible CD 4 + T cells. It is known that HIV and HTLV-I have in common a way of transmission through direct contact with certain body fluids related to infected individuals. Therefore, it is not surprising that a mono-infected person with one of these viruses can be co-infected with the other virus. In the literature, a great number of mathematical models has been presented to describe the within-host dynamics of HIV or HTLV-I mono-infection. However, the within-host dynamics of HIV/HTLV-I co-infection has not been modeled. In this paper, we develop a new within-host HIV/HTLV-I co-infection model. The model includes the impact of Cytotoxic T lymphocytes (CTLs) immune response, which is important to control the progression of viral co-infection. The model describes the interaction between susceptible CD 4 + T cells, silent HIV-infected cells, active HIV-infected cells, silent HTLV-infected cells, Tax-expressing HTLV-infected cells, free HIV particles, HIV-specific CTLs and HTLV-specific CTLs. We first show the nonnegativity and boundedness of the model's solutions and then we calculate all possible equilibria. We derive the threshold parameters which govern the existence and stability of all equilibria of the model. We prove the global asymptotic stability of all equilibria by utilizing Lyapunov function and LaSalle's invariance principle. We have presented numerical simulations to illustrate the effectiveness of our main results. In addition, we discuss the effect of HTLV-I infection on the HIV-infected patients and vice versa. [ABSTRACT FROM AUTHOR]

In clinical practice, many cirrhosis scores based on alanine aminotransferase (ALT) levels exist. Although the most recent direct acting antivirals (DAAs) reduce fibrosis and ALT levels, the Hepatitis C virus (HCV) is not always removed. In this paper, we study a mathematical model of the HCV virus, which takes into account the role of the immune system, to investigate the ALT behavior during therapy. We find five equilibrium points and analyze their stability. A sufficient condition for global asymptotical stability of the infection-free equilibrium is obtained and local asymptotical stability conditions are given for the immune-free infection and cytotoxic T lymphocytes (CTL) response equilibria. The stability of the infection equilibrium with the full immune response is numerically performed. [ABSTRACT FROM AUTHOR]

This paper investigates the stochastic HTLV-I infection model with CTL immune response, and the corresponding deterministic model has two basic reproduction numbers. We consider the nonlinear CTL immune response for the interaction between the virus and the CTL immune cells. Firstly, for the theoretical needs of system dynamical behavior, we prove that the stochastic model solution is positive and global. In addition, we obtain the existence of ergodic stationary distribution by stochastic Lyapunov functions. Meanwhile, sufficient condition for the extinction of the stochastic system is acquired. Reasonably, the dynamical behavior of deterministic model is included in our result of stochastic model when the white noise disappears. [ABSTRACT FROM AUTHOR]

In this paper, we study a fractional-order model with time-delay to describe the dynamics of Ebola virus infection with cytotoxic T-lymphocyte (CTL) response in vivo. The time-delay is introduced in the CTL response term to represent time required to stimulate the immune system. Based on fractional Laplace transform, some conditions on stability and Hopf bifurcation are derived for the model. The analysis shows that the fractional-order with time-delay can effectively enrich the dynamics and strengthen the stability condition of fractional-order infection model. Finally, the derived theoretical results are justified by some numerical simulations. [ABSTRACT FROM AUTHOR]

It is beyond dispute that cytotoxic T-lymphocytes (CTLs) exert a vital function in the host's antiviral defense mechanism. With the idea of the above factor and the logistic proliferation of CD4 + T-cells, we establish a HTLV-I (human T-cell leukemia virus type-I) mathematical model. First, two threshold parameters ℛ 0 and ℛ c (the basic reproduction numbers for viral infection and CTL immune response, respectively) are obtained. Second, sufficient criteria for local and global asymptotic stabilities of the feasible equilibria of the model are deduced, respectively. Third, the sensitivity analyses of ℛ 0 and ℛ c are performed to better understand the effective strategies for HTLV-I infection. Finally, not only numerical simulations are given to illustrate the stability conclusions, but also the biological significance is stated. [ABSTRACT FROM AUTHOR]

This paper studies the dynamical behavior of an HIV-1 infection model with saturated virus-target and infected-target incidences with Cytotoxic T Lymphocyte (CTL) immune response. The model is incorporated by two types of intracellular distributed time delays. The model generalizes all the existing HIV-1 infection models with cell-to-cell transmission presented in the literature by considering saturated incidence rate and the effect of CTL immune response. The existence and global stability of all steady states of the model are determined by two parameters, the basic reproduction number () and the CTL immune response activation number (). By using suitable Lyapunov functionals, we show that if , then the infection-free steady state is globally asymptotically stable; if , then the CTL-inactivated infection steady state is globally asymptotically stable; if , then the CTL-activated infection steady state is globally asymptotically stable. Using MATLAB we conduct some numerical simulations to confirm our results. The effect of the saturated incidence of the HIV-1 dynamics is shown. [ABSTRACT FROM AUTHOR]